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The paper proposes a new approach to gradient porous composites based on the Ti3Al(Si)C2 MAX phase. This approach is based on the production of preceramic paper with the different content of the powder filler based on MAX phases and their spark plasma sintering. The analysis of the microstructure and phase composition is conducted for these composites. It is shown that the obtained composites have a clear interface between layers with different porosity. It is found that the content of organic components in preceramic paper affects the phase composition of the fabricated composites. The MAX phase content in dense and porous layers is 86 and 56 vol.%, respectively. Microhardness measurements performed in the composite cross-section show the hardness of 600 to 800 HV, depending on the layer porosity and phase composition. [ABSTRACT FROM AUTHOR]

A wide range of applications are possible with paper-based analytical devices, which are low priced, easy to fabricate and operate, and require no specialized equipment. Paper-based microfluidics offers the design of miniaturized POC devices to be applied in the health, environment, food, and energy sector employing the ASSURED (Affordable, Sensitive, Specific, User-friendly, Rapid and Robust, Equipment free and Deliverable to end users) principle of WHO. Therefore, this field is growing very rapidly and ample research is being done. This review focuses on fabrication and detection techniques reported to date. Additionally, this review emphasises on the application of this technology in the area of medical diagnosis, energy generation, environmental monitoring, and food quality control. This review also presents the theoretical analysis of fluid flow in porous media for the efficient handling and control of fluids. The limitations of PAD have also been discussed with an emphasis to concern on the transformation of such devices from laboratory to the consumer. [ABSTRACT FROM AUTHOR]

The impact of fluid inertia on fracture flow dynamics, particularly under high-velocity conditions, has emerged as a critical consideration in petroleum engineering and related fields. This review paper investigates the profound effects of inertia-dominated nonlinear flow, a phenomenon increasingly recognised for its significant influence on fluid dynamics in rock fractures. Given the prevalence and importance of such flows in field applications, neglecting fluid inertial effects is no longer justifiable. A comprehensive investigation into these effects is essential for advancing our understanding of fracture flow mechanisms and optimising engineering practices. This review aims to thoroughly analyse the impact of fluid inertia on applications in hydraulic fracturing. It offers an in-depth discussion of how fluid inertia affects critical aspects of crack propagation, fracture diagnostics, proppant transport and settlement, and fines migration. Additionally, this paper identifies and explores four main factors that influence the fluid inertia effect in fracture flows: fracture roughness, intersections and dead ends within the fracture network, variations in contact area and fracture aperture, and the role of shear displacement. The review provides valuable insights into the complex interplay between fluid inertia and fracture flow dynamics by elucidating these factors. [ABSTRACT FROM AUTHOR]

Rock permeability is a critical parameter for assessing rock's ability to facilitate fluid flow. The pressure pulse decay method, characterized by its short testing duration and high accuracy, is widely employed for permeability testing of low-permeable rocks. This method acquires pressure differential data by conducting experiments on regular-shaped samples. Due to the theoretical solution's requirements (cross-sectional area and length), this method cannot be applied to rocks that are challenging to shape into regular samples, such as soft rock and soft coal. In this paper, a novel permeability determination method based on the numerical simulation of inverse problem is proposed. This method involves constructing a mathematical model that accurately describes the entire process of determining permeability using the pressure pulse decay method. The sample's pressure difference data over time is used as a penalty function, and the sample permeability is calculated by inverse problem numerical simulation. Specifically, a computation strategy is introduced to determine the initial range for permeability, aiming to avoid locally optimal issues in the inverse problem numerical simulation. Utilizing the new model, forward and inverse problem numerical simulations were conducted. The pressure difference decay data obtained from these calculations closely match the laboratory-measured data for regular samples, with correlation coefficient (R2) reaching 0.992 and 0.990, respectively. The permeability calculated by inverse simulation is determined to be 0.28 mD, showing minimal deviation from the theoretically derived permeability. This demonstrates the accuracy of the proposed model in describing the experimental process of the pressure pulse decay method and the precision of the obtaining permeability parameters. Furthermore, when applied to numerical experiments with irregular-shaped samples, the inverse simulation yields pressure difference data that closely matches the experimental data. The established new method effectively addresses limitations posed by the shape of samples, providing a novel approach for measuring rock permeability. The convenience of numerical experiments also offers a new and efficient means to investigate the competitive effects of permeability influencing factors. This provides promising applications in unconventional gas development, depleted reservoir carbon dioxide storage, and geological hydrogen storage, among other fields. Highlights: A mathematical model is developed to accurately describe gas mass transfer behaviour during the permeability testing by the transient method. A computational method for calculating permeability based on numerical solution is proposed. The new method proposed in this paper solves the limitation of the traditional method for the shape of the test sample. [ABSTRACT FROM AUTHOR]

The European Physical Journal: Special Topics presents a collection of fifteen papers focusing on recent advancements in composite materials and structures for energy applications. The papers cover topics such as microfluidics-integrated smart acoustic metamaterials, dusty tetra-hybrid Casson nanofluid flow, thermosolutal convection of Cu/water micropolar nanofluid, and the mechanical behavior of electroactive polymers in thermal environments. Other studies include the synthesis and sintering of ZrB2, plasma-enhanced electrodes for hydro-oxy fuel generators, and the relationship between water injection volume and liquid injection pressure in pipeline deformation. The research explores various aspects of materials science and engineering, offering insights into innovative applications and advancements in the field. [Extracted from the article]

The paper is devoted to the study of magnetic properties of magnetic colloids placed in porous media. The importance of this study is due to the development of new applications of such media. The paper presents the results of an experimental study of the temperature and frequency dependences of the magnetic susceptibility of magnetic colloids on different bases placed in a porous medium. For this purpose, a kerosene-based magnetic colloid and a water-based magnetic colloid were used. White electrocorundum was used as a porous medium. Magnetic susceptibility was studied by the bridge method in a wide range of frequencies and temperatures. It was found that the frequency and temperature dependences of magnetic susceptibility of bulk and magnetic colloids placed in porous media significantly differ depending on the pore size. The explanation of the obtained results is based on the assumption of the influence of surface forces on the relaxation processes of the magnetic moment of colloidal particles. [ABSTRACT FROM AUTHOR]

This paper aims to derive the motion equations for a small-scale flexoelectric-multilayer plate and move deep through its vibrational response to several determining variable variations. Flexoelectricity indicates the electrical polarization induction in response to the non-uniform strain gradient. As moving toward small scales, the importance and the role of this property comes more to the picture. The under-examination structure is fabricated of three layers; a mid-layer which is assumed to be composed of the porous exponential and power law-functionally graded materials, two flexoelectric face sheets, and the Vlasov foundation. The motion equations are derived mathematically based on the new EP of porous material, Hamilton's principle, and modified couple stress theory. Utilizing the new EP power law besides evaluating the influence of the variables, length scale parameter, materials composition, geometrical characteristics, porosity, foundation parameter, and boundary conditions (B.C.s) on the dimensionless natural frequency (DNF) of such a sandwich model is the novelty of this paper. It is revealed that the lateral ratio enhancement causes DNF and stiffness reduction in the model. Furthermore, among all considered B.C.s, simply support and clamped support refer to the lowest and the highest DNF, respectively. The content of the recent paper serves as a good source to provide a better understanding of the vibrational response of high stiffness-to-weight ratio structures to different variable variations. [ABSTRACT FROM AUTHOR]

In this paper, we establish the boundary regularity results for viscosity solutions of fully nonlinear degenerate/singular parabolic equations of the form u t - x n γ F (D 2 u , x , t) = f , where γ < 1 . These equations are motivated by the porous media type or fast diffusion type equations. We show the boundary C 1 , α -regularity of functions in their solutions class and the boundary C 2 , α -regularity of viscosity solutions. As an application, we derive the global regularity results and the solvability of the Cauchy–Dirichlet problems. [ABSTRACT FROM AUTHOR]

The paper summarizes the main provisions of Alexander Spirin's concept on the possible role of RNA, molecular machines, and molecular colonies in the emergence of life, including (1) the role of the capability of polyribonucleotides of spontaneous rearrangements and recombinations in the generation of RNA molecules and development of their structure, as well as in the early replication of RNA; (2) the principle of operation of molecular machines powered by the energy of Brownian motion and the need for their emergence to solve the problem of unwinding double-stranded molecules formed as a result of the complementary copying of RNA; (3) the role of molecular colonies formed during the replication of RNA in porous media as a mode of compartmentalization and as a prerequisite for the evolution in the precellular RNA world. [ABSTRACT FROM AUTHOR]

Due to the wide variety of porous materials, studying their properties can be laborious. This paper proposes a porous structure generation algorithm for molecular dynamics simulation, which simplifies and accelerates the study of porous material properties. The algorithm can generate a porous system with a specified porosity, pore size, and solid matrix distribution in the material. The algorithm successfully generates morphology similar to that of experimental samples. This is demonstrated through the example of NiTi intermetallic compound. [ABSTRACT FROM AUTHOR]

The Richards equation is ubiquitous in the modelling of flows in porous media. It serves as a model in its own right, but also as a stepping stone to more complex models of multiphase flows. Despite its relative simplicity, it features many challenges from a computational point of view due to the nonsmooth and degenerate nature of the nonlinear state functions. In this paper, we replace these functions with regularized (smooth and nondegenerate) counterparts where the amount of added regularization is controlled by a single regularization parameter. We introduce a set of a simple a posteriori error estimators that we use to adaptively steer the regularization and linearization. In particular, we stop the iterative linearization when the corresponding estimator is dominated by the regularization estimator and adaptively choose the regularization parameter so that the regularization estimator does not dominate the discretization one. The full adaptive algorithm is tested on a suite of numerical examples adapted from recent works on improving the robustness of solvers for the Richards equation and on benchmark cases. [ABSTRACT FROM AUTHOR]

The widely used Darcy's law specifies a linear relation between the Darcy velocity of fluid flow and the pressure gradient that drives the flow. However, studies have shown that Darcy velocity can exhibit a nonlinear dependence on the pressure gradient in low-permeability porous media such as clay and shale when the pressure gradient is adequately low. This phenomenon is referred to as low-velocity non-Darcian flow or pre-Darcy flow. This paper provides a comprehensive review of the theories, experimental data, and modeling methods for pre-Darcy flow in low-permeability porous media. The review begins by outlining the fundamental mechanisms underlying pre-Darcy flow that regulate the unique characteristics such as nonlinear dependence of the Darcy velocity on the pressure gradient and its relevance to fluid–rock interactions. The review then proceeds to present a thorough compilation of experimental investigations performed in various low-permeability geomaterials including tight sandstones, shales, and clays. Next, empirical and theoretical models and simulation methods that have been developed to fit and interpret experimental data are reviewed. Finally, the review underscores the challenges encountered in conducting and interpreting pre-Darcy flow experiments and suggests future research directions. By analyzing previous experimental investigations, this review aims to offer a valuable resource for researchers and practitioners seeking to enhance their understanding of fluid dynamics in low-permeability geomaterials. This provides insights into the application of pre-Darcy flow in numerous natural and engineered processes such as shale oil and gas recovery, contaminant transport in low-permeability aquifers, and geological disposal of nuclear waste. [ABSTRACT FROM AUTHOR]

Most research currently is limited to isotropic or porous materials reinforced by graphene platelets (GPLs). However, functionally graded materials (FGMs) made of two different material constituents offer many advantages in terms of durability, strength, high-temperature resistance, and design flexibility. Therefore, a new FGM model reinforced by GPLs (GPL-reinforced FGM) is proposed to enhance the performance of nanoplate structures. This paper presents analytical solutions for buckling and static bending problems of the GPL-reinforced FGM nanoplates with surface stress effects placed on a Pasternak elastic foundation. Three variation laws of the FGM (i.e., P-FGM, E-FGM, and S-FGM) combined with four GPL patterns (i.e., UD, FG-O, FG-X, and FG-V) are studied. The governing equations of the nanoplate resting on the elastic foundation are derived based on the principle of minimum total potential energy, Reddy's third-order shear deformation theory (TSDT), nonlocal strain gradient (NSG) theory (NSGT), and Gurtin–Murdoch surface elasticity theory (SET). The Navier technique is then utilized to determine the critical buckling load, deflection, and stress components of the nanoplate. The influence of material parameters, NSG parameters, surface energy parameters, and elastic foundation parameters on the static buckling and bending behaviors of the GPL-reinforced FGM nanoplate is investigated. [ABSTRACT FROM AUTHOR]

In this paper, we consider the propagation of chaos on bounded convex domains. Under some suitable assumptions, the empirical measure of a large number of particles on a bounded domain is shown to approximate the solution of the porous medium equation. Moreover, the propagation of chaos is derived. [ABSTRACT FROM AUTHOR]

Polymer flooding is a prominent chemical enhanced oil recovery (CEOR) method that involves the injection of polymer solution into the oil reservoirs to improve the sweep efficiency and maximize the ultimate oil recovery. Selecting an appropriate polymer type, molecular weight, and concentration is crucial for success of any polymer flooding project. This paper studies the flow behavior of HPAM-based EOR polymers with different molecular weights through porous media. Dynamic adsorption and injectivity tests were performed through 5 Darcies sandpacks using polymer solutions prepared with low (LM; 8–10 MDa) and high (HM; 20–25 MDa) molecular weight polymers. Polymer solutions with different target viscosity values of 7, 15 and 30 cP were flooded through sandpacks at the reservoir temperature of 80 ºC and pore pressure of 1000 psi. The results showed that HM solutions with different target viscosity have higher polymer retention through sandpacks compared to LM solutions. Furthermore, results of residual resistance factor (RRF) measurements were in line with dynamic adsorption tests results. That is, permeability reduction due to irreversible polymer retention was higher when HM polymer solutions were injected. Furthermore, the results showed that although the resistance factor (RF) and in-situ viscosity of HM and LM polymers are in the same range, however, shear thickening regime becomes pronounced in the case of HM polymer with higher target viscosity. Polymer relaxation time measurements, and consequently, Deborah number calculations were performed to describe the shear thickening behavior by polymers viscoelastic characteristics. Results demonstrate that occurrence of shear thickening regime is controlled by Deborah number which is a function of polymer molecular weight, polymer concentration and injection rate. These results shed light on the importance of the selection of optimal polymer molecular weight and concentration during the design of polymer flooding projects. [ABSTRACT FROM AUTHOR]

Lightweight porous structural materials have excellent energy absorption performance, and their application are gradually appeared. This paper takes the shock-absorbing material of nuclear equipment transportation casks as the starting point, and manufactures an orthogonal trapezoidal aluminum honeycomb by welding (WOTAH). The mechanical properties with different cell thicknesses and cell size ratios under different impact loads are studied through experimental and simulation methods, and the deformation process and energy absorption performance of the materials are obtained. The energy absorption performance of materials under quasi-static loading was investigated using plastic deformation theory and compared with experimental results. Based on the experimental results, the least squares method was used for data fitting to obtain the C-S dynamic constitutive relationship of the material. The equivalent structure was used to replace the honeycomb structure for simulation, and the influence of strain rate effect and structural size on material properties was further studied. Through the above mechanical performance analysis and comparison with wood, it is shown that WOTHA has feasible for the application of nuclear equipment impact limiter. [ABSTRACT FROM AUTHOR]

The paper presents the results of investigation into the effects of the composition of a nonwetting liquid (distilled water, physiological solution, and doxorubicin solution) on the kinetics of outflow from hydrophobized Fluka 100 C18 silica gel. A series of measurements was taken regarding the filling of and discharge from the investigated systems in the temperature range of 5 to 40°C with the waiting time between cycles 10–1000 s. Values were obtained for the fraction of the liquid that failed to flow out of a porous material as a function of time and temperature, and also the functions of pore size distribution were recovered for the retained liquid. A reduction was found in the fraction of the retained liquid with increase in temperature and the waiting time. It follows from the obtained results that the determination of the outflow kinetics for a doxorubicin solution with a concentration of up to 1 μM can be carried out without using a medicinal drug. [ABSTRACT FROM AUTHOR]

This paper investigates the effects on the behavior of a saturated porous material of an evolving microstructure induced by the mass exchange between the solid and the fluid phases saturating the porous network, using two-scale asymptotic expansions. A thermodynamically consistent model of the fluid physics flowing through the porous network is proposed first, describing microstructure variations to be captured implicitly via the level set method. The two-scale asymptotic expansions method is then applied to obtain an upscaled model capable to account for mass transfer. This last is proven to depend not only on the gradient of the macroscopic forces, such as the fluid pressure and the chemical potential, but also on the average velocity of the solid–fluid interface. Numerical simulations are carried out using the finite element method in order to evaluate the relative weight of the new terms introduced. [ABSTRACT FROM AUTHOR]

In this paper, the capillary is divided into several regions, and the effective pore radius is proposed. The relationship between the effective hole radius and the maximum radius is analyzed. The fractal models of fractal flow rate, average velocity and effective permeability of power-law fluid flow in fractal soil composed of circular cross section capillaries are derived. The effects of different power exponent, viscosity coefficient and fractal dimension on the average flow velocity and effective permeability model are analyzed, and the comparative analysis of different sections is carried out. The reasonable calculation results of the fractal model given in this paper verify the correctness of the model. The introduction of the effective pore radius concept and the derivation of fractal models have advanced our ability to characterize and predict flow behavior. We anticipate that these findings will stimulate further research and practical applications in various domains, benefiting both scientific knowledge and technological advancements. [ABSTRACT FROM AUTHOR]

The paper discusses the accuracy parameters of measuring the most important structural characteristics of porous and disperse materials, such as specific adsorption of gases, specific surface area, specific pore volume and pore size. The performance of sorbents, catalysts, and membranes in the chemical and petroleum industries, including purification of substances and materials, depends on the values of these characteristics. It has been established that in order to ensure mutual recognition of the national standards and certificates of calibrations and measurements of the porosity characteristics of solid substances, performed by the national metrology institutes, it is required to organize and successfully participate in three international key comparisons under the auspices of the Consultative Committee for Amount of Substance: Metrology in Chemistry and Biology of the International Bureau of Weights and Measures. The paper presents the results of participation of the national metrology institutes and designated organizations of Germany, China, Japan, Brazil, Turkey and Russia in three international key comparisons in the field of measuring specific adsorption of gases (e.g., nitrogen, argon, krypton) and specific surface area of solids (e.g., zeolite, silica, and alumina). Carrying out the optimal number of comparisons makes it possible to register in the Key Comparison Database of the International Bureau of Weights and Measures the calibration and measurement capabilities of the national metrology institutes of the participating countries for various matrices in a wide range of measurements of specific adsorption of gases (0.001–25 mol/kg) and specific surface area of solids (0.1–1500 m2/g). Based on the results of the three international key comparisons, 18 calibration and measurement capabilities of the Russian participant (D.I. Mendeleev Institute for Metrology) were entered into the Key Comparison Database, two of which are currently undergoing examination. These entries include reference standards produced by the Institute. A comparative analysis of the results of measuring specific surface area of solids using nitrogen and krypton as adsorbates was performed. It has been established that the uncertainty of the results of measuring specific surface area is significantly less when using krypton as an adsorbate for specific surface areas less than 1 m2/g. This is caused by the higher values of the relative pressure of krypton compared to nitrogen. The use by the calibration and testing laboratories in Russia of the reference standards of sorption properties, included in the Key Comparison Database of the International Bureau of Weights and Measures, will ensure metrological traceability in the field of measuring porosity characteristics. [ABSTRACT FROM AUTHOR]

In this paper, an innovative approach for enhancing fluid transport modeling in porous media is presented, which finds application in various fields, including subsurface reservoir modeling. Fluid flow models are typically solved numerically by addressing a system of partial differential equations (PDEs) using methods such as finite difference and finite volume. However, these processes can be computationally demanding, particularly when aiming for high precision on a fine scale. Researchers have increasingly turned to machine learning to explore solutions for PDEs in order to improve simulation efficiency. The proposed method combines an adaptive multi-scale strategy with generative adversarial networks (GAN) to increase simulation efficiency on a fine scale. The devised model, called simulation enhancement GAN (SE-GAN), takes coarse-scale simulation results as input and generates fine-scale results in conjunction with the provided petrophysical properties. With this new approach, a deep learning model is trained to map coarse-scale results to fine-scale outcomes, rather than directly solving the fluid flow model. Case studies reveal that SE-GAN can achieve a significant improvement in accuracy while reducing computational time compared to the original fine-scale simulation solver. A comprehensive evaluation of numerical experiments is conducted to elucidate the benefits and limitations of this method. The potential of SE-GAN in accelerating the numerical solver for reservoir simulations is also demonstrated. [ABSTRACT FROM AUTHOR]

Over the past few decades, pore-network models (PNMs) have emerged as a pivotal tool in the investigation of fluid flow within porous media. The crux of PNM lies in the extraction of the topological structure of porous media, as abstracted from geological scans, commonly referred to as the pore network. Conventional methods for pore-network extraction rely on pixel-based techniques and necessitate high-quality images to accurately capture pore information. In recent times, the flashlight search medial axis (FSMA) algorithm has been introduced, offering a novel approach to extract pore networks within continuous spatial domains. This innovation enables the algorithm to operate independently of specific pixels, thereby significantly reducing computational complexity. Building upon the foundational principles of the FSMA algorithm, this paper presents an efficient search algorithm in conjunction with string methods. This algorithm facilitates the precise determination of pore and throat center locations within porous media using a minimal number of computational points and can accurately compute the positions of pore medians. Furthermore, this algorithm can effectively circumvent the issue of dead-end pores encountered in the FSMA algorithm, a feature of paramount importance in the study of multiphase flow within porous media. [ABSTRACT FROM AUTHOR]

In this paper, three-dimensional numerical algorithm is constructed to simulate the behavior of the Brinkman-Forchheimer flow and thermal fields. Numerical results of velocity, pressure and temperature are obtained by applying the efficient modified two-grid marker and cell (MAC) algorithm on staggered grids with the second-order backward difference formula (BDF2) time approximation. The modified-upwind idea is introduced to convective heat transfer equations for improving accuracy without any numerical oscillation. The second-order convergence rate can be achieved for pressure, velocity and temperature of considered three-dimensional model. Some numerical experiments are presented to illustrate the efficiency of algorithm. The numerical example with analytical solution is used to validate the effectiveness and accuracy of the algorithm by comparing with the results of traditional MAC algorithm. A time-dependent test is proposed to show a detailed sensitivity analysis to indicate the influence of parameters including the ε , Forchheimer number, Brinkman number and thermal diffusivity on the physical properties of Brinkman-Forchheimer flow and heat transfer in porous media. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is to investigate the axisymmetric bending response of functionally graded porous (FGP) circular plates. The material properties are changed continuously in the thickness direction of the plate. Three distinct porosity distributions uniform, symmetric and monolithic are employed. The effect of porosity on the axisymmetric bending analysis of circular plates is examined parametrically. In this study, clamped and roller supports which commonly serve to achieve ideal boundary conditions in numerous engineering applications are used. The finite element method is employed for numerical analysis. The principal of the potential energy is used to obtain the governing equations. To generate the model of the FGP circular plates, an eight-node quadratic quadrilateral element with two degrees of freedom on each node is utilized. The results of this study are confirmed by the existing published literature. A good agreement between the results of the presented model and the previous literature has been observed. The results of the present study show that plate deflection increases with the increase of the porosity coefficient and the ratio of radius to thickness of circular plates. By increasing the porosity coefficient, the displacement values of the plates made of uniform porosity distribution is effected more than those of other porosity distributions. [ABSTRACT FROM AUTHOR]

The paper presents the results of a study on the hydration heat of ultralight cementitious foams envisaged as insulation materials for building envelopes. The examined porous foam-cement material was additionally enhanced by embedded microencapsulated phase change material (PCM) to improve the desired thermal properties of the material. The heat emission and heat flow were measured at 20 °C and 30 °C for 168 h using the isothermal calorimeter. The experimental study comprised composites with dry densities of 240 kg m−3 and 480 kg m−3, two concentrations of protein-based foaming agent (2% and 4%) and two dosages of the embedded PCM material (10% and 20%). The reference composite without PCM was also tested. The effect of the necessary admixtures used to achieve the stability of ultralight cementitious foams was also examined. The results showed that hydration in ultralight foam-cement composites is retarded, and the values of heat released are lower than those of the paste used to produce the composites. In this regard, the main factors contributing to the lower heat released and its lower rate are the excess water from the foam, the dosage of the foaming agent and the admixtures introduced to achieve the stability of the ultralight composite. The stabiliser was found to be the most retarding admixture. Considering PCM, which was added at 10% and 20% of the paste volume, a rather low influence on the course of the hydration process was observed due to the overall composition of ultralight cementitious foams specially modified for each assumed content of PCM. [ABSTRACT FROM AUTHOR]

The efficient characterization of material properties of porous multi-phase sintered steels by instrumental indentation is still an open question. To the authors' knowledge, so far only a characterization of single-phase porous sintered steel by nanoindenation has been reported in literature. This paper for the first time offers a study about the applicability of microindentation techniques for characterizing the matrix material in a multi-phase sintered steel. This preliminary study is motivated by the relatively wide availability of necessary equipment, and simplicity of material identification procedures. Herein, a dual-phase ferrite/bainite Astaloy steel with 9% porosity is studied. Various commonly used methods for the reconstruction of stress–strain curves from microindentation data are considered, whereby both Vickers and spherical tips are used. In addition, some homogeneous solid materials are investigated to better asses the performance of applied identification procedures. Two approaches for the mesoscale identification of the considered sintered steel are attempted. The first one is based on the identification of individual material phases, while in the other one the homogenization of the metallic matrix is adopted. To assess the reliability of obtained parameters, the direct numerical simulation of representative volume elements of realistic steel microstructure subjected to uniaxial tension is conducted. Numerical results are compared with the data from the macroscopic uniaxial tensile test. The obtained results indicate that microindentation is adequate for the identification of elastic properties of individual material phases, but results for local plastic parameters are largely inconclusive and a further analysis is needed, focusing on applying smaller forces and investigating the influence of pores on identification results. Nevertheless, it seems that macroscopic stress–strain curves could be captured more accurately by the methodology based on the matrix homogenization if relatively large indentation forces are applied. [ABSTRACT FROM AUTHOR]

Graphene-nanosheet-based highly porous magnetite nanocomposites (GN-HPMNs) have been prepared using a simple solvothermal method and used as an immobilization matrix for the fabrication of a solid-state electrochemiluminescence (ECL) sensor on paper-based chips. Highly porous FeO nanocrystal clusters were coated with acrylate and wrapped tightly on the skeleton of graphene nanosheets. The structures and sizes of the GN-HPMNs could be tuned by varying the proportions of the solvents ethylene glycol and diethylene glycol. Then, the relatively highly porous ones with an average diameter of about 65 nm were combined with Nafion to form composite films on an electrode surface for immobilization of Ru(bpy) (bpy is 2,2′-bipyridine). Because of their porosity, negatively charged surface, and cooperative characteristics of magnetic nanomaterials and graphene, under an external magnetic field, the GN-HPMNs ensured effective immobilization, excellent electron transfer, and long-term stability of Ru(bpy) in the composite film. The sensor developed exhibited excellent reproducibility with a relative standard deviation of 0.65 % for 30 continuous cycles. It was found to be much more favorable for detecting compounds containing tertiary amino groups and DNAs with guanine and adenine. A detection limit (signal-to-noise ratio of 3) of 5.0 nM was obtained for tripropylamine. As an application example, 0.5 nM single-nucleotide mismatch could be detected. This was the first attempt to introduce magnetic nanomaterials and an external magnetic field into paper-based chips. The sensor developed has the advantages of high sensitivity, good stability, and wide potential applicability as well as simplicity, low cost, and good disposability. [Figure not available: see fulltext.] [ABSTRACT FROM AUTHOR]

The fabrication concept for a low-cost sensor device using reduced graphene oxide (rGO) as the sensing material on a porous paper substrate is presented. The sensors were characterized using conductivity and capacitance measurements, atomic force microscopy and X-ray photoelectron spectroscopy. The effects of different reducing agents, graphene oxide (GO) flake size and film thickness were studied. The sensor was sensitive to NO, and devices based on a thin (10-nm) hydrazine-reduced GO layer had the best sensitivity, reaching a 70 % reduction in resistance after 10 min of exposure to 10 ppm NO. The sensitivity was high enough for the detection of sub-parts per million levels of NO. Desorption of gas molecules, i.e. the recovery of the sensor, could be accelerated by UV irradiation. The structure and preparation of the sensor are simple and up-scalable, allowing their fabrication in bulk quantities, and the fabrication concept can be applied to other materials, too. [Figure not available: see fulltext.] [ABSTRACT FROM AUTHOR]

In this paper, the entropy generation of natural convection Jeffrey fluid flow through an inclined porous channel is investigated by taking into account the impact of angled magnetic field, Soret parameter, thermal radiation, and Hall current. On the basis of simplified assumptions, the governing equations are transformed into dimensionless equations by using suitable transformations, and the spectral quasi-linearization method (SQLM) is used for the numerical solution. Graphs are utilized to address the effects of new thermophysical parameters. The calculations reveal that increasing the Soret parameter, inclination angle, Hall parameter, magnetic parameter, and Jeffrey fluid parameter induces an increase in entropy generation. Conversely, it decreases as the radiation parameter and channel angle of inclination increase. [ABSTRACT FROM AUTHOR]

Reservoir simulation is crucial for understanding the flow response in underground reservoirs, and it significantly helps reduce uncertainties in geological characterization and optimize methodologies for field development strategies. However, providing efficient and accurate solutions for the strong heterogeneity remains challenging, as most of the discretization methods cannot handle this complexity. In this work, we perform a comprehensive assessment of various numerical linearization techniques employed in reservoir simulation, particularly focusing on the performance of the nonlinear solver for problem dealing with fluid flow in porous media. The primary linearization methods examined are finite difference central (FDC), finite forward difference (FDF), and operator-based linearization (OBL). These methods are rigorously analyzed and compared in terms of their accuracy, computational efficiency, and adaptability to changing reservoir conditions. The results demonstrate that each method has distinct strengths and limitations. The FDC method is more accurate particularly in complex simulations where strong heterogeneity are introduced but is generally slower in convergence. The OBL on the other hand, is more efficient and converges quickly, which makes it suitable for scenarios with limited computational resources and simple physics, while the FDF method provides a balanced combination of precision and computational speed, contingent upon careful step size management of the derivative estimations. This paper aims to guide the selection of appropriate linearization techniques for enhancing nonlinear solvers' accuracy and efficiency in reservoir simulation. [ABSTRACT FROM AUTHOR]

In this paper, we consider the complex flows when all three regimes pre-Darcy, Darcy and post-Darcy may be present in different portions of a same domain. We unify all three flow regimes under mathematics formulation. We describe the flow of a single-phase fluid in by a nonlinear degenerate system of density and momentum. A mixed finite element method is proposed for the approximation of the solution of the above system. The stabilit1y of the approximations are proved; the error estimates are derived for the numerical approximations for both continuous and discrete time procedures. The continuous dependence of numerical solutions on physical parameters are demonstrated. Experimental studies are presented regarding convergence rates and showing the dependence of the solution on the physical parameters. [ABSTRACT FROM AUTHOR]

In this paper, the mathematical model of heat and porous media equations being considered in fractional form. The Laplace residual power series method and the Laplace Adomian decomposition technique are used to compare the solutions of the fractional heat transfer and porous media equations. For this reason, a few examples are presented to understand the fractional heat transfer and porous media equations in its more accurate form. The results show the simple and sophisticated procedures of the two proposed analytical approaches, where partial differential equations are considered with fractional derivatives. The outcomes of the described methods demonstrate that they have an accurate algorithm to construct with exceptionally precise cost calculation capabilities. The obtained results are presented through tables and graphs and the approximate results are found in great contact with exact solutions. [ABSTRACT FROM AUTHOR]

In this paper, the coupled linear theory of thermoviscoelasticity for porous materials is considered in which the coupled phenomenon of the following four mechanical principles is proposed: the deformation of the skeleton of a porous solid, the volume fraction concept of the pore network, Darcy's law for the flow of a fluid through a porous medium, and Fourier's law of thermal conduction. The governing systems of equations of motion and steady vibrations are proposed. The fundamental solution of the system of steady vibration equations is presented explicitly by means of elementary functions, and its basic properties are established. By virtue of Green's identity the uniqueness theorems for the classical solutions of the basic internal and external boundary value problems (BVPs) of steady vibrations are proved. Then, the surface and volume potentials are presented and their basic properties are given. Finally, the existence theorems for classical solutions of the above-mentioned BVPs are proved by means of the potential method (boundary integral equation method) and the theory of singular integral equations. [ABSTRACT FROM AUTHOR]

The 1D moisture diffusivity of porous materials may strongly depend on the content of moisture in the materials, varying over an order of magnitude or more. In this paper we present a new model from which the diffusivity can be evaluated, using the pore size distribution and water absorption coefficient. We point out that this is a more efficient approach than the standard Boltzmann–Matano (BM) method, because measurements of pore curves and water absorption are much shorter and rather accurate compared to moisture profile experiments needed in the BM method. As an example, we apply our model to two samples of a ceramic brick for which experimental data on both pore curves and moisture profiles had been measured. A very good quantitative agreement in the diffusivity is obtained for early stage profiles. For later stages, however, the model predicts three to four times higher diffusivity than the BM method. The reasons for this discrepancy are discussed and further tasks to validate the effectiveness of the new model are proposed. We also compare our model with the pore models of Burdine and Mualem. [ABSTRACT FROM AUTHOR]

This paper presents and discusses the results obtained by the participants to the benchmark described in de Hoop et al, Comput. Geosci. (2024). The benchmark uses a model for CO2 geological storage and focuses on the coupling between two-phase flow and geochemistry. Several test cases of various levels of difficulty are proposed, both in one and two spatial dimensions. Six teams participated in the benchmark, each with their own simulation code, though not all teams attempted all the cases. The codes used by the participants are described, and the results obtained on the various test cases are compared, as well as the performance of the codes. It is shown that the results obtained are widely consistent, giving a good level of confidence in the outcome of the benchmark. The general complexity of two-phase flow coupled with chemical reactions altering porous media means that some differences between the codes remain. Besides, from the convergence study, it is clear that the two-dimensional problem has a relatively high sensitivity to a spatial resolution which adds to the complexity. [ABSTRACT FROM AUTHOR]

This paper investigates the contact problem of an elastic layer that is perfectly attached to a porous half-space by two rigid flat punches with collinear symmetry. Using integral transformation, the problem is condensed to a singular integral equation of the Cauchy type. Then, the exact expressions for the surface contact stress and surface interface displacement are provided. By using the Gauss–Chebyshev technique, the integral equations are solved numerically, and the variations of the unknown contact stresses and deformations for different parameters are addressed. The results indicate that stress concentration is typically higher on the outer edge of the contact area compared to the inner edge. This also explains why surface damage is more likely to occur on the outer edge in elastic and poroelastic materials. Due to the interaction between the two punches, there will be a superposition of normal displacements at the center. The deformation or bulging at the center can be managed by adjusting the parameter values, allowing the engineered material to fulfill its intended purpose. The potential applications of these research findings encompass safeguarding porous structures against contact-related deformation and damage. [ABSTRACT FROM AUTHOR]

A novel analysis of the pulsatile nano-blood flow through a sinusoidal wavy channel, emphasizing the significance of diverse influences in the modelling, is investigated in this paper. This study examines the collective effects of slip boundary conditions, magnetic field, porosity, channel waviness, nanoparticle concentration, and heat source on nano-blood flow in a two-dimensional wavy channel. In contrast to prior research that assumed a constant pulsatile pressure gradient during channel waviness, this innovative study introduces a variable pressure gradient that significantly influences several associated parameters. The mathematical model characterising nano-blood flow in a horizontally wavy channel is solved using the perturbation technique. Analytical solutions for fundamental variables such as stream function, velocity, wall shear stress, pressure gradient, and temperature are visually depicted across different physical parameter values. The findings obtained for various parameter values in the given problem demonstrate a significant influence of the amplitude ratio parameter of channel waviness, Hartmann number of the magnetic field, permeability parameter of the porous medium, Knudsen number due to the slip boundary, volume fraction of nanoparticles, radiation parameter, Prandtl number, and heat source parameters on the flow dynamics. The simulations provide valuable insights into the decrease in velocity with increasing magnetic field and its increase with increasing permeability and slip parameters. Additionally, the temperature increases with increasing nanoparticle volume fraction and radiation parameter, while it decreases with increasing Prandtl number. [ABSTRACT FROM AUTHOR]

This paper presents an analytical formulation to investigate functionally graded porous beams' nonlinear thermal buckling performance under various boundary conditions. The current model incorporates innovative cinematic techniques with the focus on the stretching effect and the iteration techniques. The material properties of the porous FG beams are temperature-dependent and vary according to a simple power-law distribution. The validity of the present theory' results is confirmed by comparing them with those obtained by other researchers. The findings demonstrate that the critical buckling temperature in TD and TID ranges from 1.03 to 1.27% for a uniform distribution and 1 to 1.47% for linear and non-linear distributions. Conversely, for regular porosity variation, the critical buckling temperatures fluctuate between 0.99 and 1.74%, and between 0.99 and 1.59% for porosity variation. Furthermore, the influence of boundary conditions becomes more pronounced when the nonlinear temperature difference is high. [ABSTRACT FROM AUTHOR]

This paper focuses on the evaluation of the macroscopic elastoplastic mechanical behavior of porous rock-like geomaterials. It is assumed that the porous matrix of the material contains randomly distributed spherical micro-voids, and the solid phase obeys to the Drucker–Prager criterion, then its yield behavior is described by an analytical strength homogenization criterion of porous media. To consider the non-associated plastic flow, a fractional non-orthogonality of plastic flow is introduced without using a plastic potential. Then the interaction of two different damage mechanisms is incorporated in the constitutive relation, the first is the damage induced by plastic deformation and the other is the influence of void nucleation, growth and coalescence during the deformation process. Within this framework, a series of numerical studies is conducted to clarify the influence of initial porosity and its evolution on macroscopic mechanical properties. The numerical results show that the proposed model is able to capture the main mechanical features of the studied porous rock-like material. [ABSTRACT FROM AUTHOR]

A new strategy was developed to build a CO2-philic/hydrophilic surfactant by combining the common free radical polymerization and the grafting modification technology, and a brush polymer was synthesized with poly(vinyl acetate)(PVAc) based copolymer as the CO2-philic group (as the main chain) and the methoxy poly(ethylene glycol) (mPEG) as the hydrophilic part (as the branched chain) (PVAc-g-mPEG). The CO2-philic ability can be controlled by adjusting the chain length of the CO2-philic fragment. The results indicate that PVAc-g-mPEG has excellent surfactant activity, and can emulsify the CO2/H2O system to obtain the CO2-in-water (C/W) high interval phase emulsion (HIPE 80%, v/v), which can remain stable for more than 20 h. If using the monomers/crosslinking agent solution instead of water, the highly porous monolithic materials will be obtained after the continuous phase is polymerized. In this paper, polyacrylamide (PAM) and poly(acrylamide/diethyl aminoethyl methacrylate) (PADM)-based porous monolithic materials were prepared. These materials were used to remove bovine serum albumin (BSA, as the model matter) from the solution, and the results indicated that PAM-based porous monolithic materials had almost no enrichment capacity for protein, while PADM-based porous monolithic materials can adsorb BSA up to 129.3 mg/g. [ABSTRACT FROM AUTHOR]

The digital core and pore network model (PNM) are the basis of studying porous media. At present, the voxel-based maximal ball (MB) method has been widely used in the construction of PNM. However, due to the dependence on discrete data and the fuzziness of size definition, the PNM by using this method may not be accurate. The construction of PNM is essentially a geometric problem. Therefore, a computational geometry method was proposed in this paper to construct the PNM. A grid-based core surface model was constructed by using the moving cubes (MC) algorithm, the maximal inscribed ball of the grid space was extracted by using the computational geometry method, and a PNM was built by judging 12 types of dependency relationships of the master and servant spheres in the inscribed ball. Finally, combined with Berea sandstone, the physical parameters of cores obtained by the proposed method and the MB method were compared. The throat length results show that the proposed algorithm has improved the defect of small throat length when the MB method is used to partition core pore space. Meanwhile, the results of other parameters tend to be consistent, which proves the reliability of the proposed algorithm. Besides, by comparing the seepage simulation results of the two methods with the physical experiments, it was proved that the permeability calculated by the method in this paper is closer to the measured value of the physical experiment than that by the MB method. [ABSTRACT FROM AUTHOR]

In this paper, the forced vibration of a functionally porous sandwich beam with a viscoelastic core has been investigated. The upper and lower layers of the beam are made of functionally porous materials, and the porosity gradient in porous layers is distributed through their thickness. The core of the beam is made of viscoelastic materials. The Golla–Hughes–McTavish (GHM) model is employed to simulate the viscoelastic behavior of the core. Applying the Hamilton principle and Euler–Bernoulli theory, the governing equation of motion is obtained for a simply supported beam. The Newmark method is applied to solve the time-dependent differential equation of the beam. The results are compared with data from the literature review and a commercial finite element software. In the Results and Discussion section of the paper, a parametric study is performed to investigate the effects of porosity and viscoelastic parameters on the forced vibration of the beam. Finally, the results obtained by the GHM model are compared with the Kelvin–Voigt model for constant and variable input frequencies. According to the results, both models predict identical behavior for constant input frequency. However, the GHM model provides better results for the case of variable input frequency. [ABSTRACT FROM AUTHOR]

Numerical modeling of multiphase flow phenomena in fractured porous media has always been a hot topic in recent years. Projection-based embedded discrete fracture model (pEDFM) is a recently developed modeling framework that has been shown to resolve some limitations of the commonly used embedded discrete fracture model (EDFM). However, determining the continuous projection path of fracture networks and adding needed fracture-fracture (f-f) connections in the previous pEDFM workflows is too complicated to construct a generic and easy-to-program algorithm. Although there are several studies about applications of pEDFM to numerically model the flow problems in fractured porous media, a generic pEDFM workflow has not been truly formed. Therefore, this theoretically advanced numerical modeling framework of flow problems in fractured porous media has not been widely noticed and applied. To construct a generic pEDFM workflow, this paper first illustrates that the fracture projection path obtained by the micro-translation method can achieve acceptable simulation accuracy for flow across a high-conductivity fracture, then a generic and easy-to-program non-projective method is developed to model low-conductivity fractures. Numerical examples verify that the developed pEDFM workflow can effectively handle low-conductivity fractures (e.g. flow barriers) in general cases, thus avoiding the difficulty of developing a generic algorithm for constructing a continuous projection path for the low-conductivity fracture. It is also verified that the new pEDFM workflow with the addition of simple f-f connections can solve the cases that classical pEDFM solves with significant errors. Furthermore, it achieves similar or better computational accuracy than the pEDFM modified by adding complex f-f connections, thus avoiding the difficulty of developing a generic algorithm for constructing these additional f-f connections. Overall, the first generic pEDFM workflow is developed in this paper, which significantly improves the practicability of pEDFM and may induce more applications of pEDFM in numerical modeling of flow problems in fractured porous media. [ABSTRACT FROM AUTHOR]

In this paper, a new functionally graded material (FGM) porous sandwich plate analysis model considering pores with only four variables is proposed. It is applied to the nonlinear bending of two different types of FGM porous sandwich plates under mechanical loading, and the bending of two different types of FGM porous sandwich plates is compared. The governing equations are obtained through the principle of virtual work. The simple supported FGM porous sandwich plates are solved using the Navier method. The obtained numerical results are compared with the results in the literature to verify the accuracy of the theory in this paper. Finally, the effects of volume fraction index, porosity, layer thickness ratio, side-thickness ratio and symmetry on the mechanical bending properties of FGM porous sandwich plates are studied in detail. By comparing the bending characteristics of two types of FGM porous sandwich plates under different influencing factors, it is found that the bending characteristics of different FGM porous sandwich plate types are also very different. This has great guiding significance for the design of FGM porous sandwich plates. [ABSTRACT FROM AUTHOR]

The heat pulse (flash) experiment is a well-known, widely used method to determine thermal diffusivity. However, for heterogeneous, highly porous materials, neither the measurement nor the evaluation methodologies are straightforward. In the present paper, we focus on two open-cell carbon foam types, differing in their porosity but having the same sample size. Recent experiments showed that a non-Fourier behavior, called 'over-diffusive' propagation, can be present for such a complex structure. The (continuum) Guyer–Krumhansl equation stands as a promising candidate to model such transient thermal behavior. In order to obtain a reliable evaluation and thus reliable thermal parameters, we utilize a novel, state-of-the-art evaluation procedure developed recently using an analytical solution of the Guyer–Krumhansl equation. Based on our observations, it turned out that the presence of high porosity alone is necessary but not satisfactory for non-Fourier behavior. Additionally, the mentioned non-Fourier effects are porosity-dependent; however, porous samples can also follow the Fourier law on a particular time scale. These data serve as a basis to properly identify the characteristic heat transfer mechanisms and their corresponding time scales, which altogether result in the present non-Fourier behavior. Based on these, we determined the validity region of Fourier's law in respect of time scales. [ABSTRACT FROM AUTHOR]

Porous media reconstruction is quite significant in the fields of environmental supervision, oil and natural gas engineering, biomedicine and material engineering. The traditional numerical reconstruction methods such as multi-point statistics (MPS) are based on the statistical characteristics of training images (TIs), but the reconstruction quality may be unsatisfactory and the process is time-consuming. Recently, with the rapid development of deep learning, its powerful ability in predicting features has been used to reconstruct porous media. Generative adversarial network (GAN) is one of the generative methods of deep learning, which is derived from the two-person zero-sum game through the confrontation between the generator and discriminator. However, the traditional GAN cannot pay special attention to the effective features in learning, and the degradation problem easily occurs with the increase of layer numbers. Besides, high-resolution (HR) and large FOV (field of view) are usually contradictory for physical imaging equipment. Therefore, in practical experiments, due to the limitations of the resolution of imaging equipment and the sample size, it is difficult to obtain large-scale HR images of porous media physically. At this point, numerical super-resolution (SR) reconstruction seems to be a cost-efficient way. In this paper, residual networks and attention mechanisms are combined with single-image GAN (SinGAN), which can learn the structural characteristics of porous media from a low-resolution (LR) 3D image, and then reconstruct 3D HR or large-scale images of porous media. Comparison to some other numerical methods has proved that our method can reconstruct high-quality HR images with practicability and effectiveness. [ABSTRACT FROM AUTHOR]

In this paper, Polyethylene Terephthalate Glycol (PETG) has been used as a novel thermoplastic thermo-responsive Shape Memory Polymer (SMP) with biocompatibility, excellent printability, cost efficiency, and transparency for the 3D/4D printing of porous structures by material extrusion. The high deformability of PETG allows for programming without an increase in temperature or the need for additional operations. This enabled the use of PETG for the Cold Programming (CP) of ordered porous shape memory structures, made possible by material extrusion printing technology. The porous samples were printed employing three patterns and two porosity percentages. The programming operation was performed at ambient temperature by applying different amounts of pre-strains under constrained and unconstrained compression modes. The constrained test was conducted using a mandrel and a matrix for exerting pure volume reduction (pure packing). The shape recovery test was accomplished above the glass transition temperature (Tg), and the fixity and recovery ratios were recorded. Employing 3D printing provided the ability to manufacture porous thermoplastic SMP structures with highly controllable pores geometry and sizes for different porosity percentages. The results showed that the combination of the uniform strain distribution in the porous structures with the help of the 3D printing process and CP on the new PETG SMP makes it possible to achieve high deformation in the glassy region, resulting in a complete shape recovery for two lozenge and vertical patterns. Among all specimens, constrained specimens by horizontal pattern had the highest fixity ratio of 90.7%. However, low fixity ratios in CP can be justified considering the existence of two stages of spring-back and structural relaxation after unloading, resulting from the elastic and viscoelastic behavior. Increasing Infill Density (ID) along with the constrained test (pure packing) improved the shape fixity. The existence of higher mechanical constraints and harsher localized deformation are speculated to be the case for this observation. Applying higher deformations (40 to 80%), for both designed tests, brought about a weakness in the shape memory performance, while it improved for 100% volume reduction. [ABSTRACT FROM AUTHOR]

The paper analyzes the possibility of creating a titanium porous fiber material for implants, which is made of fibers of various transverse sizes and has gradient pore architecture. The architecture of the porous space, structure, and mechanical characteristics of such material have been studied. It is shown that the strength of the porous fiber material can be improved by increasing the temperature of diffusion bonding and by performing hydrogen heat treatment. The specifics of the mechanical behavior and fracture of the material samples were studied by performing a fixed-end bending test. [ABSTRACT FROM AUTHOR]

The direct emission of coal mine methane caused serious environmental pollution and resource waste. To improve the methane utilization, the porous media burner was regarded as an efficient method. In this paper, the bluff body was proposed to combine with porous media to optimize the combustion characteristics. The effects of bluff body position, size and shape on the temperature distribution and gas emission were studied at different operating conditions. The results indicated that the position of the bluff body greatly influenced the combustion characteristics, and the maximum temperature of 1295 K was obtained at the position of 62 mm. The increase of the bluff body diameter promoted the flame moving to the burner outlet. And the combustion temperature increased first and then decreased when the bluff body height increased. Moreover, the CO and NOx emissions at the height of 20 mm reached 31 and 16.8 ppm respectively. The combustion temperature was significantly improved by increasing the equivalence ratio and velocity. Compared with the single porous media, the addition of the bluff body increased the combustion temperature and reduced the CO emission by 11%. [ABSTRACT FROM AUTHOR]

In the paper we consider the development of an algorithm for predicting the catalytic activity of porous materials based on the concept of transition state shape selectivity (TSSS). We evaluated catalytic activity of single-wall carbon nanotubes (SWCNT) in the Diels–Alder reaction on example of interaction cyclopentadiene with acrylonitrile, maleic anhydride, and piperylene with ethylene. We have viewed the stabilization of transition states (TS) on the surface of nanotubes of various diameters. As a quantitative value of TS stabilization energy, we applied the calculated value of the adsorption energy of TS with frozen structure on SWCNT, which was found using Material Studio 8.0 program. It is shown that the dependence of the adsorption energy on the diameter of the nanotubes has an extremum for all the considered TS, and the maximum adsorption energy is achieved when the TS is placed inside a tube of a certain diameter. Obviously, this diameter can be assumed optimal for achieving the greatest catalytic effect. Depending on the size of the TS of the considered reactions, the optimal diameter of the nanotubes is 9–11 Å. Also, we found, that for the reaction cyclopentadiene with acrylonitrile, the difference between linear dimensions of TS for endo- and exo-isomers formation is noticeable, which suggests the possibility of selective catalysis by SWCNT. [ABSTRACT FROM AUTHOR]